As is well known, some internal combustion engines for vehicles or the like clean up exhaust gas using a three-way catalyst that simultaneously enhances oxidation of unburned components (HC and CO) and reduction of nitrogen oxides (NOx). In order to maintain the purification performance of such a three-way catalyst, it is necessary to combust fuel at an air-fuel ratio that is close to the stoichiometric air-fuel ratio. Therefore, an internal combustion engine equipped with a three-way catalyst performs feedback control such that the air-fuel ratio seeks the stoichiometric air-fuel ratio, while detecting an air-fuel ratio obtained based on oxygen concentration of exhaust gas.
Recently, a three-way catalyst provided with oxygen storage capacity has been commercialized. Such a three-way catalyst stores excessive oxygen when the air-fuel ratio is leaner than the stoichiometric air-fuel ratio and the oxygen concentration in exhaust gas is high, and releases the stored oxygen to compensate for shortage of oxygen when the air-fuel ratio is richer than the stoichiometric air-fuel ratio and the oxygen concentration is low. This suitably maintains exhaust gas purification capacity for the catalyst even when the air-fuel ratio temporarily deviates from the stoichiometric air-fuel ratio. However, because of limited oxygen storage capacity of the catalyst, it is necessary to keep the quantity of oxygen stored by the catalyst in a certain range (e.g., about half of its maximum capacity) to ensure that the catalyst can store or release oxygen on a steady basis.
Therefore, control apparatuses that perform air-fuel ratio feedback by PI control or PID control have been proposed for internal combustion engines, as disclosed by, e.g., Japanese Laid-Open Patent Publication No. 9-280038. Such a control apparatus controls air-fuel ratio by an integral action on a difference detected between a target and actual air-fuel ratios. A PI control system, for example, corrects an air-fuel ratio based on a correction amount obtained using the following formula (1):Air-fuel ratio correction amount=(Air-fuel ratio difference)×(Proportional gain)+(Integrated air-fuel ratio difference)×(Integral gain)  (1)
In the formula (1), the first term of the right-hand side [(Air-fuel ratio difference)×(Proportional gain)] is a proportional term, based on which deviation of air-fuel ratio from the stoichiometric air-fuel ratio is compensated. The second term [(Integrated air-fuel ratio difference)×(Integral gain)] is an integral term, based on which steady state deviation of the air-fuel ratio is compensated. More specifically, the integral term corrects air-fuel ratio in such a way as to equalize an integrated quantity of oxygen newly stored by a three-way catalyst with an integrated quantity of oxygen released from the catalyst. Therefore, integral correction of air-fuel ratio stably maintains the quantity of oxygen stored by a three-way catalyst.
It should be noted, however, that an integral term for integral correction of air-fuel ratio is determined based on the history of air-fuel ratios irrespective of the actual intake air amount or air-fuel ratio, which may lead to erroneous air-fuel ratio correction, as described below.
When an internal combustion engine whose air-fuel ratio tends to greatly deviate from the stoichiometric air-fuel ratio is operating at a high intake air amount, this may cause a relatively large absolute value of the integral term. When the engine is decelerated in this state, and the intake air amount is significantly reduced, a high absolute value of the integral term recorded so far at a high load is directly applied immediately after the deceleration, possibly leading to excessive correction of the air-fuel ratio.
Also, when the internal combustion engine is operating at a lower load and lean air-fuel ratio after the engine has been running at a richer air-fuel ratio than the stoichiometric air-fuel ratio for an extended period, the air-fuel ratio will be corrected to be excessively lean immediately since a correction using the integral term makes the air-fuel ratio even leaner. This may lead to misfire.
The erroneous correction of the air-fuel ratio by an integral term can be prevented to some extent by setting the integral gain so that the absolute value of the integral term is relatively small. Setting the integral gain at a small value, however, may deteriorate air-fuel ratio feedback convergence, possibly leading to problems, e.g., deteriorated exhaust emissions.